Interest calculations are a fundamental part of financial management, affecting everything from personal savings to large loans. One specific method of calculating interest is the daily interest formula.
This formula is particularly important for products that accrue interest on a daily basis, such as credit cards and certain types of loans. This article will explain the daily interest formula, how to calculate it, and its practical applications.
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Daily Interest Formula
The daily interest formula is used to determine how much interest accrues on a principal balance each day.
The basic formula is:
Daily Interest = Principal × Annual Interest Rate % /(100*365)
the Daily Interest Rate expressed as a percentage is given by the formula
Daily Interest Rate % = Annual Interest Rate % / 365
Where:
- Principal: The initial amount of money on which interest is calculated
- Annual Interest Rate %: The yearly interest rate expressed as a percentage. Annual Interest Rate is also called Annual Percentage Rate or APR.
- 365: The number of days in a year
As an example for an annual interest rate of 10%, the daily interest rate is 0.027 %.
Formula for Compounding Daily Interest
If the interest is compounded daily, each day’s interest is added to the principal before the next day’s interest is calculated. This leads to exponential growth of the principal over time. The formula for the future value A after n days of compounding daily interest is:
A = P × (1 + r/365)n
Where:
- A = the future value of the investment/loan
- P = the principal investment/loan amount
- r = the annual interest rate expressed as a decimal number
- n = the time the money is invested/borrowed for in days
- 365 = number of days in a year
What is Daily Interest?
Daily interest refers to the interest charged or earned on a principal amount over a single day. Unlike other interest calculations, which might be monthly or annually, daily interest compounds more frequently, leading to a different accumulation pattern.
This method is commonly used in:
- Credit Cards: Most credit cards calculate interest on the outstanding balance daily.
- Short-Term Loans: Payday loans and certain types of personal loans often use daily interest calculations.
- Savings Accounts: Some savings accounts use daily compounding to calculate interest earnings.